Regina Calculation Engine
Public Member Functions | Static Public Member Functions | Protected Member Functions | Friends
regina::NAngleStructure Class Reference

Represents an angle structure on a triangulation. More...

#include <angle/nanglestructure.h>

Inheritance diagram for regina::NAngleStructure:
regina::ShareableObject regina::NFilePropertyReader regina::boost::noncopyable

List of all members.

Public Member Functions

 NAngleStructure (NTriangulation *triang, NAngleStructureVector *newVector)
 Creates a new angle structure on the given triangulation with the given coordinate vector.
virtual ~NAngleStructure ()
 Destroys this angle structure.
NAngleStructureclone () const
 Creates a newly allocated clone of this angle structure.
NRational getAngle (unsigned long tetIndex, int edgePair) const
 Returns the requested angle in this angle structure.
NTriangulationgetTriangulation () const
 Returns the triangulation on which this angle structure lies.
bool isStrict () const
 Determines whether this is a strict angle structure.
bool isTaut () const
 Determines whether this is a taut angle structure.
bool isVeering () const
 Determines whether this is a veering structure.
void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream.
void writeXMLData (std::ostream &out) const
 Writes a chunk of XML containing this angle structure and all of its properties.
void writeToFile (NFile &out) const
 Writes this angle structure and all of its properties to the given old-style binary file.
- Public Member Functions inherited from regina::ShareableObject
 ShareableObject ()
 Default constructor that does nothing.
virtual ~ShareableObject ()
 Default destructor that does nothing.
virtual void writeTextLong (std::ostream &out) const
 Writes this object in long text format to the given output stream.
std::string toString () const
 Returns the output from writeTextShort() as a string.
std::string toStringLong () const
 Returns the output from writeTextLong() as a string.
- Public Member Functions inherited from regina::NFilePropertyReader
virtual ~NFilePropertyReader ()
 Default destructor that does nothing.

Static Public Member Functions

static NAngleStructurereadFromFile (NFile &in, NTriangulation *triangulation)
 Reads an angle structure and all its properties from the given old-style binary file.

Protected Member Functions

virtual void readIndividualProperty (NFile &infile, unsigned propType)
 Reads an individual property from an old-style binary file.
void calculateType () const
 Calculates the structure type (strict or taut) and stores it as a property.

Friends

class regina::NXMLAngleStructureReader

Detailed Description

Represents an angle structure on a triangulation.

Once the underlying triangulation changes, this angle structure is no longer valid.

Test:
Included in the test suite.

Constructor & Destructor Documentation

regina::NAngleStructure::NAngleStructure ( NTriangulation triang,
NAngleStructureVector newVector 
)
inline

Creates a new angle structure on the given triangulation with the given coordinate vector.

Python:
Not present.
Parameters:
triangthe triangulation on which this angle structure lies.
newVectora vector containing the individual angles in the angle structure.
regina::NAngleStructure::~NAngleStructure ( )
inlinevirtual

Destroys this angle structure.

The underlying vector of angles will also be deallocated.


Member Function Documentation

void regina::NAngleStructure::calculateType ( ) const
protected

Calculates the structure type (strict or taut) and stores it as a property.

NAngleStructure* regina::NAngleStructure::clone ( ) const

Creates a newly allocated clone of this angle structure.

Returns:
a clone of this angle structure.
NRational regina::NAngleStructure::getAngle ( unsigned long  tetIndex,
int  edgePair 
) const

Returns the requested angle in this angle structure.

The angle returned will be scaled down; the actual angle is the returned value multiplied by pi.

Parameters:
tetIndexthe index in the triangulation of the tetrahedron in which the requested angle lives; this should be between 0 and NTriangulation::getNumberOfTetrahedra()-1 inclusive.
edgePairthe number of the vertex splitting representing the pair of edges holding the requested angle; this should be between 0 and 2 inclusive. See vertexSplit and vertexSplitDefn for details regarding vertex splittings.
Returns:
the requested angle scaled down by pi.
NTriangulation * regina::NAngleStructure::getTriangulation ( ) const
inline

Returns the triangulation on which this angle structure lies.

Returns:
the underlying triangulation.
bool regina::NAngleStructure::isStrict ( ) const
inline

Determines whether this is a strict angle structure.

A strict angle structure has all angles strictly between (not including) 0 and pi.

Returns:
true if and only if this is a strict angle structure.
bool regina::NAngleStructure::isTaut ( ) const
inline

Determines whether this is a taut angle structure.

A taut angle structure contains only angles 0 and pi.

Here we use the Kang-Rubinstein definition of a taut angle structure [1], which is based on the angles alone. In his original paper [2], Lackenby has an extra condition whereby 2-faces of the triangulation must have consistent coorientations, which we do not enforce here.

[1] E. Kang and J. H. Rubinstein, "Ideal triangulations of 3-manifolds II; Taut and angle structures", Algebr. Geom. Topol. 5 (2005), pp. 1505-1533.

[2] M. Lackenby, "Taut ideal triangulations of 3-manifolds", Geom. Topol. 4 (2000), pp. 369-395.

Returns:
true if and only if this is a taut structure.
bool regina::NAngleStructure::isVeering ( ) const
inline

Determines whether this is a veering structure.

A veering structure is taut angle structure with additional strong combinatorial constraints, which we do not outline here. For a definition, see C. D. Hodgson, J. H. Rubinstein, H. Segerman, and S. Tillmann, "Veering triangulations admit strict angle structures", Geom. Topol., 15 (2011), pp. 2073-2089.

Note that the Hodgson et al. definition is slightly more general than Agol's veering taut triangulations from his original paper: I. Agol, " Ideal triangulations of pseudo-Anosov mapping tori", in "Topology and Geometry in Dimension Three", volume 560 of Contemp. Math., pp. 1-17, Amer. Math. Soc., 2011. This mirrors the way in which the Kang-Rubinstein definition of taut angle structure is slightly more general than Lackenby's. See the Hodgson et al. paper for full details and comparisons between the two settings.

If this angle structure is not taut, or if the underlying triangulation is non-orientable, then this routine will return false.

Returns:
true if and only if this is a veering structure.
static NAngleStructure* regina::NAngleStructure::readFromFile ( NFile in,
NTriangulation triangulation 
)
static

Reads an angle structure and all its properties from the given old-style binary file.

This routine reads precisely what writeToFile() writes.

Deprecated:
For the preferred way of reading angle structures from file, see class NXMLAngleStructureReader instead.
Precondition:
The given file is currently opened for reading.
Python:
Not present.
Parameters:
inthe file from which to read.
triangulationthe triangulation on which this angle structure will lie.
Returns:
a newly allocated angle structure containing the information read from file.
virtual void regina::NAngleStructure::readIndividualProperty ( NFile infile,
unsigned  propType 
)
protectedvirtual

Reads an individual property from an old-style binary file.

The property type and bookmarking details should not read; merely the contents of the property that are written to file between NFile::writePropertyHeader() and NFile::writePropertyFooter(). See the NFile::writePropertyHeader() notes for details.

The property type of the property to be read will be passed in propType. If the property type is unrecognised, this routine should simply do nothing and return. If the property type is recognised, this routine should read the property and process it accordingly (e.g., store it in whatever data object is currently being read).

Parameters:
infilethe file from which to read the property. This should be open for reading and at the position immediately after writePropertyHeader() would have been called during the corresponding write operation.
propTypethe property type of the property about to be read.

Implements regina::NFilePropertyReader.

void regina::NAngleStructure::writeTextShort ( std::ostream &  out) const
virtual

Writes this object in short text format to the given output stream.

The output should fit on a single line and no newline should be written.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
outthe output stream to which to write.

Implements regina::ShareableObject.

void regina::NAngleStructure::writeToFile ( NFile out) const

Writes this angle structure and all of its properties to the given old-style binary file.

This routine writes precisely what readFromFile() reads.

Deprecated:
For the preferred way to write data to file, see writeXMLData() instead.
Precondition:
The given file is currently opened for writing.
Python:
Not present.
Parameters:
outthe file to which to write.
void regina::NAngleStructure::writeXMLData ( std::ostream &  out) const

Writes a chunk of XML containing this angle structure and all of its properties.

This routine will be called from within NAngleStructureList::writeXMLPacketData().

Python:
Not present.
Parameters:
outthe output stream to which the XML should be written.

The documentation for this class was generated from the following file:

Copyright © 1999-2012, The Regina development team
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).